using temperature-sensitive paint
Steffen Risius · Walter H. Beck · Christian Klein · Ulrich Henne · Alexander Wagner
Abstract Heat loads on spacecraft travelling at hypersonic speed are of major interest for their designers. Several tests using temperature-sensitive paints (TSP) have been carried out in long duration shock tunnels to determine these heat loads; generally paint layers were thin, so that certain as-sumptions could be invoked to enable a good estimate of the thermal parameterρck(a material property) to be
ob-tained – the value of this parameter is needed to determine heat loads from the TSP. Very few measurements have been carried out in impulse facilities (viz. shock tunnels such as the High Enthalpy Shock Tunnel (HEG)), where test times are much shorter. Presented here are TSP temperature mea-surements and subsequently derived heat loads on a ramp model placed in a hypersonic flow in HEG (specific enthalpy
h0≈3.3 MJ kg−1, Mach numberM=7.4, temperatureT = 277 K, densityρ∞=11 g/m3). A number of fluorescence
in-tensity images were acquired, from which, with the help of calibration data, temperature field data on the model surface were determined. From these the heat load into the surface was calculated, using an assumption of a 1D, semi-infinite heat transfer model. ρck for the paint was determined us-ing an insitucalibration with a Medtherm coaxial thermo-couple mounted on the model; Medtherm ρck is known. Finally presented are sources of various measurement un-certainties, arising from: (1) estimation ofρck(2) intensity measurement in the chosen interrogation area (3) paint time response.
Steffen Risius [email protected]
Institute of Aerodynamics and Flow Technology, German Aerospace Center (DLR), Bunsenstr. 10, 37073 G¨ottingen, Germany
First published by Springer-Verlag GmbH Germany 2017 Exp Fluids (2017) 58:117
doi:10.1007/s00348-017-2393-z
1 Introduction
Test models coated with temperature-sensitive paints (TSP) have been used in the DLR over recent years in various wind tunnels (WT) to measure temperatures and/or temperature changes on the model surface - see Costantini et al. (2015); Engler et al. (2000); Fey et al. (2013); Klein et al. (2005, 2013, 2014); Streit et al. (2011) for results with TSP (and also with its pressure analogue PSP – this is also referenced here since many details and difficulties of the technique are common to both TSP and PSP). Absolute temperatures as a function of time during the flow are needed to determine heat transfer from the (usually much hotter) test gas into the model surface – this will be the main topic of interest in this paper, and will be further elucidated in following sections. (Measurement of temperature changes alone can be used to determine boundary layer transition in some WT flows – this will not be further discussed here, but an example can be seen in Costantini et al. (2015).) Since objects (missiles, space transporters and capsules, . . . ) moving at supersonic and especially hypersonic speeds through some atmospheric gas are exposed to very high gas temperatures behind the generated bow shock, it is essential for the optimization of the external aerodynamics and for the design of the insula-tion of these vehicles to be able to determine the heat loads that prevail during the various stages of the ascent and de-scent trajectories. The WT used are often so-called impulse facilities (such as shock tubes or tunnels), giving test times in some cases only in the millisecond (or even microsecond) range; this provides a particular challenge for the TSP tech-nique to be able to carry out measurements in these short times. In recent years, an increased interest (Gardner et al., 2014; Gregory et al., 2014) in the study of instationary flow physical phenomena (transition, turbulence, separation, heat transfer) has led to a requirement for fast acquisition sys-tems: high speed cameras, high power (pulsed) LED’s and, above all, paints with sufficiently fast response times to
en-able these instationary or short-duration phenomena to be captured quantitatively and faithfully.
Some of the first measurements using TSP (and PSP) in a shock tunnel to measure heat loads (and pressure distribu-tion) on a test model were carried out in the early 2000’s by the research group of Prof. Asai (then at NAL Chofu, Japan, now at Tohoku University in Sendai, Japan): see, for exam-ple Nakakita et al. (2003); Ohmi et al. (2006), wherein other work in hypersonic flows is also referenced. The 0.44 m Hy-personic Shock Tunnel (NAL-HST) has two different oper-ation modes to generate the shock: the Long Duroper-ation Mode (1) using fast-acting valves or the High Enthalpy Mode (2) using a bursting diaphragm, with both modes delivering flows with different durations of about 20 ms and 1 ms to 5 ms, re-spectively. The TSP measurements cited in the above-men-tioned papers were carried out using operation mode (2). The paint consisted of a Ru(phen) luminophore embedded in a polyacrylic acid binder. Very thin layers (≤1 µm) were applied, and the assumption was then made that the temper-ature measured by TSP differs only slightly from that under the layer on the model surface – this difference was esti-mated to be only about 4 %. Hence, one could take values for the thermal parameter (ρck) for the model material (known) rather than that of the TSP layer (unknown) to calculate heat load from the measured TSP temperature. The thin TSP lay-ers have the disadvantage, however, that the fluorescence in-tensity is quite low, although this is to some extent com-pensated by the long flow test times of around 20 ms. In a recent paper by Peng et al. (2016) the results from PSP and TSP measurements carried out in a long-duration hypersonic tunnel have also been presented.
In this paper a different approach is suggested for mea-surements in the DLR High Enthalpy Shock Tunnel (HEG) with its much shorter test times (<10 ms). The DLR Eu-based paint OV322 active (see later) used here has a high fluorescence intensity, but is much thicker (80 µm) than that used in long duration tunnels, so that the assumptions for
ρckmade there do not apply here. Here a Medtherm coaxial
thermocouple (see later) is flush mounted with the coated test surface, so that temperature measurements from both TSP and Medtherm are available; one can use contiguous regions for temperatures from Medtherm and TSP to do an insitu calibration ofρckfor the TSP layer, using the known value for the Medtherm. Measurement uncertainties and er-rors are discussed in great detail in the present paper. (Whilst preparing this manuscript, a measurement using TSP in the High Enthalpy Shock Tunnel HIEST had been presented at the recent 55’th AIAA Aerospace Sciences Meeting: Na-gayama et al. (2017).)
Flows in hypersonic facilities present several challenges in adapting the TSP technique to these difficult environments, especially in HEG with its test times of less than 10 ms; however, these challenges have been met and addressed, and
are discussed in a recent paper which was presented at the 2015 AIAA SciTech Meeting (Beck et al., 2015). TSP based on a different (blue-shifted) luminophore has been studied by Martinez Schramm et al. (2015) and used successfully in HEG to visualize boundary layer transition (Ozawa et al., 2015) and to examine internal SCRAMJET flows (Laurence et al., 2012).
Presented here are temperature measurements and de-rived heat loads using TSP on a ramp model placed in a hypersonic flow in HEG in order to demonstrate the feasi-bility of measuring heat transfer into the model surface un-der these conditions. Results from one only available HEG run are presented. A discussion of derived ρck values for the paint is presented, along with a more detailed analysis of measurement errors arising from uncertainties inρck val-ues, statistical fluctuation in the interrogation area and the finite time response of the paint relative to the camera shut-ter window.
2 Experimental section
The HEG tunnel, the test model (ramp) and TSP measure-ment procedure have been described in greater detail else-where (Hannemann and Martinez Schramm, 2007; Hanne-mann et al., 2008), so that only a short summary will be pre-sented here. Temperature measurements on a ramp model in a low enthalpy flow in the DLR free piston-driven shock tun-nel HEG were carried out at one location with a Medtherm thermocouple and over the whole surface which was coated with the TSP paint. The used HEG test condition XIV (Han-nemann et al., 2008) was chosen in order to minimize the effect of HEG background radiation (Beck et al., 2015) with specific enthalpyh0≈3.3 MJ kg−1, Mach numberM=7.4 and the freestream properties temperatureT∞=277 K and
densityρ∞=11 g/m3. A schematic drawing of HEG is shown
in Fig. 1.
The ramp model, consisting of a flat aluminium plate (with dimensions 80 mm×20 mm) with a sharp leading edge was placed at an angle of 15◦to the flow direction. It was coated with the DLR OV322 paint (Eu-based luminophore and polyurethane (PU) binder), which had been developed in collaboration with the University of Hohenheim (Ondrus et al., 2015). The ramp model had two small holes, one for a point-wise pressure measurement (using a KuliteR piezo-resistive pressure sensor mounted below the plate in the plate holder) and one for a point-wise temperature measurement (using the coaxial thermocouple MedthermR protruding from the holder and inserted in the ramp model hole so as to be flush-mounted with the plate surface) – see Figs. 2 and 3.
TSP fluorescence was excited with a RappR High Power LED operating at 405 nm in CW mode and the images were captured with a PhotronR HiSpeed Camera SA1 (provided by LaVisionR) running at a sampling rate of 5 kHz and with
Fig. 1 Schematic drawing of the High Enthalpy Shock Tunnel G¨ottingen, HEG. Source: Wagner et al. (2013)
Fig. 2 Block diagram (plan view) of experimental setup in HEG test section.
exposure times of 200 µs; recordings were carried out over 10 ms, so that 50 images in all were obtained.
3 Temperature determination using TSP
The quenching processes which reduce the intensity of the excited paint luminophore fluorescence I(T)are tempera-ture dependent:I(T) = f(1/T). Typically, using an
Arrhe-Fig. 3 Left: Detailed photograph of the ramp model, mounted in the test section. (Flow is from right to left.) Right: Photo of irradiated ramp model (pink color) in test section, showing camera and LED light source.
nius formulation, one obtains (Liu and Sullivan, 2005): ln I(T) I(Tre f) =Ea R 1 T − 1 Tre f (1) HereEais the activation energy for the non-radiative process
andRis the universal gas constant. In practice, Eq. 1 does not always hold exactly, so that one tends (Liu and Sulli-van, 2005) to carry out a calibration at knownT (andP) and perform a fit (e.g. polynomial) ofI(T)/I(Tre f)toT/Tre f:
I(Tre f)
I(T) = f(T/Tre f) (2)
This is the standard approach adopted here, and was carried out in the laboratory using small coupons coated with the same paint as used on the test model and then calibrated in a test rig with known test conditions (viz. temperatureT and pressurep). A calibration plot for the OV322 paint used here
is shown in Fig. 4, from which can be seen that this paint has good temperature sensitivity in the range 290 K to 340 K (ca.
−3 % K−1to−5 % K−1(Ondrus et al., 2015).1
Fig. 4 Calibration of OV322 paint: intensity ratioI(273K)/I(T)vs. temperatureT. (Source: Ondrus et al. (2015).
With this calibration plot, and assuming that the condi-tions used in the HEG test were sufficiently similar (cam-era settings, lens settings, LED light source) to those of the calibration, one needs only one reference image in HEG to obtain the temperature results for all other images; these ref-erence images in HEG are those which are obtained before gas arrival (att<1 ms) – see Fig. 5 and later discussion in Sects. 5.1 and 5.2.
4 Determination of heat loads 4.1 Temperature sensors
Measurement of heat transfer into a model surface for hy-personic flows of high enthalpy (up to 22 MJ kg−1) and short duration (down to 100 µs) places stringent requirements on the performance of the adopted temperature sensors: they must have a fast response and be able to survive the ex-treme environments of these flows (especially the high tem-peratures and, in some cases, presence of foreign particu-late matter). Over the years coaxial thermoelements have become established as the sensor of choice in HEG (and most shock tunnels) to fulfil the abovementioned require-ments. The firm Medtherm supplies these sensors, and also provides a calibration (see later) to be used for the evaluation of heat transfer from temperature measurements. Obviously, these sensors yield point-wise measurements only, so that 1The normalization with a different temperature would also be possible, which would lead to a constant multiplicative factor. See for example Ondrus et al. (2015).
a test model must be equipped with many to obtain over-all heat loads; this may be difficult, especiover-ally with some complex geometries. The advantage of a field measurement technique such as TSP lies clearly to hand.
4.2 Evaluation of heat transfer from Medtherms and TSP Following an approach suggested by Schultz and Jones (1973), with a modification by Cook and Felderman (1966), two key assumptions were made to obtain a simple relationship for determining heat transfer from temperature measurements:
1. Heat transfer into the model surface (or paint) is one-dimensional;
2. The surface is assumed to be semi-infinite in depth. Obviously these requirements are only met if the time over which measurement occurs is very short – for the typical test times in shock tunnels (<10 ms), it can be shown (Mar-tinez Schramm et al., 2015) that these assumptions are valid. Following Hannemann and Martinez Schramm (2007) (wherein a good discussion of heat transfer measurements in shock tunnels can be found), the following equation for heat trans-fer has been derived:
qw(t) = r ρck π T(t) √ t + 1 2 Z t 0 T(t)−T(τ) (t−τ)3/2 dτ (3) whereT =measured temperature,ρ=material density;c=
heat capacity;k=heat conductivity;τ=time;t= integra-tion time step. The factorρckis also known as the thermal
parameter, and is strictly a function of the (sensor) mate-rial properties only. This is not fully correct, sincecandk
may also have temperature dependence – see discussion in Sect. 5.4. Since there are no available calibration values for
ρckof the TSP paint (but see later), the approach adopted here is the following: using temperatures measured by the Medtherm sensor, and using its knownρckvalue (as
sup-plied by the manufacturer: ρck=7.95×107kg2K−2s−5), determine the heat load at its position using a discretized form of Eq. 3. Then assume that the heat load in an adjoin-ing interrogation region (see Fig. 5, to be discussed later) is the same as for the Medtherm location, so that, by adjust-ing (varyadjust-ing) theρckvalue for the TSP paint in this region,
the same heat load as for the Medtherm is determined. This is effectively an insitu calibration of the TSP paint, with the foundρckbeing assumed to be the same and applicable over all the whole coated surface.
5 Results and discussion
This section addresses the following: raw TSP results; TSP temperature results; TSP heat load results; an estimation of
the accuracy of and uncertainties in the TSP temperature and heat load results.
5.1 HEG results; TSP images (raw data)
The results from only one HEG run were available, so that measurements of reproducibility could not be carried out. The temperature (Medtherm) and adjacent pressure (Kulite) measurements at the respective sensor locations (as shown in the inset in Fig. 5 are given in Fig. 6 and Fig. 7; temper-ature is plotted as∆T(whereT0=293 K before gas arrival) as a function of time. The bump seen peaking at 2 ms in the Medtherm trace (also in the Kulite trace, but less marked) is due to the nozzle starting processes for this HEG condition. Fifty TSP images were recorded, one every 200 µs, over the 10 ms test time period. Fig. 5 shows one of these raw im-ages (with only background correction applied, but with no correction by a reference image).
Fig. 5 Average intensity (counts) in interrogation area vs. time (ms) for all 50 recorded raw images. Intensity and time error bars – note asymmetry - for early and late times are shown. A detailed discussion about the measurement uncertainty is given in Sect. 5.4.3. Inset: raw unprocessed image att=1.8 ms showing interrogation area. (Flow in the image is fromrighttoleft)
As mentioned before, and for reasons alluded to there, a small (square) interrogation region close to the Medtherm sensor location was chosen; it was situated equidistant be-tween the Medtherm and Kulite sensors, and had a size of 15×15 pixels, which corresponds to an area on the ramp of approximately 2.5 mm×2.5 mm – see inset in Fig. 5. The average (over all pixels) intensity in this region was deter-mined for all 50 images, and then plotted as a function of time, as also shown in Fig. 5. (Intensity and time error bars – note asymmetry - for early and late times are shown: for a discussion, see Sect. 5.4.3.) The abscissa time zero (origin) corresponds to the arrival of the shock wave at the end of the
driven section, at which time data recording is triggered. It can be seen that it takes about 1 ms for the test gas to arrive at the test section window; hence, for times less than 1 ms, the intensity is at a maximum, after which it subsequently drops as the model surface temperature increases.
The results att<1 ms will later be used as reference val-ues, since the conditions (viz. temperature) are well-known at these early times before the test gas has arrived. They will also be used to apply intensity distribution corrections to the results att>1 ms, allowing for various geometrical effects (camera angle and settings), and for the uneven LED illumi-nation – see Sect. 4.2. Interestingly, the bump seen clearly in the Medtherm result att=2 ms, as referred to before (see Figs. 6 and 7), appears as a change of gradient in the TSP re-sult att≈2.5 ms – see Fig. 8. This slight time shift between the Medtherm and TSP results is due to the finite response time of the TSP paint, and will be discussed in more detail in Sect. 5.4.3. The evolution (drop) of intensity is as expected from the model described by Eq. 3 and with the inherent assumptions referred to before. Note from Fig. 5 that the in-tensities after 7 ms are only about 100 counts or less, so that the accuracy of the temperature determination will be lower than at early times. This is not a serious restriction, however, since typically the customarily adopted HEG test time win-dow lies much earlier than this (around 3 ms to 4 ms) (see for example Laurence et al. (2014)); the flow at later times may be influenced by effects such as driver gas arrival and pres-ence of other disturbances such as boundary layer leakage, arrival of the contact surface or of the reflected expansion wave, and so is often not further considered.
The change in intensity distribution on the model surface over time, brought about by the increasing surface temper-ature, can be clearly seen in the four raw images shown in Fig. 8 for the timest=1.8 ms, 2.6 ms, 5.0 ms and 9.0 ms. As expected, the average intensity drops steadily. At this stage, however, without application of the reference image correc-tions referred to before, nothing can be inferred about the change of temperature as a function of time over the surface – this will be addressed in the next section. Nevertheless, one can already see some physical features: for example, a wake downstream of the Medtherm (its position is shown in Fig. 5), clearly visible att=2.6 ms. The wake most likely arises from the sensor being mounted not fully flush with the paint surface, but recessed slightly (by about 10 µm to 100 µm) below it.2Note again that the results at later times are most likely subject to disturbances which influence the state of the test gas; in spite of this, the development in in-tensity over time all the way up to 10 ms looks reasonable and believable.
2The slight dent at the sensor location is not expected to influence the temperature and heat flux measurements of the Medtherm sensor significantly, since the boundary layer thickness at the sensor location is expected to be at least one order of magnitude larger.
Fig. 6 Temperature change∆T measured by a Medtherm sensor on ramp model in this HEG run.
Fig. 7 Pressure changePmeasured by a Kulite sensor on ramp model in this HEG run.
5.2 TSP temperature results
Using the first four recorded images as reference (Tre f =
293 K), and with the help of the calibration plot shown in Fig. 4, one can then obtain temperatures over the whole model surface for all remaining 46 images. Ten results at different times (0.4 ms, 2 ms, 3 ms, 4 ms, 5 ms, 6 ms, 7 ms, 8 ms, 9 ms and 10 ms) are shown in Fig. 9, where the first image (att=0.4 ms) is a typical reference image before gas arrival. (The apparent asymmetry (e.g. see direction of the streak wakes) is due to non-parallel alignment of the wedge relative to the flow direction, which can already be inferred from the non-horizontal orientation of the raw images seen in Figs. 5 and 8.)
Quite clearly one can see the development of tempera-ture on the surface over time. (The result att=0.4 ms cor-responds to a reference image, viz. before gas arrival.) Re-sults fort>5 ms suggest temperatures in excess of 330 K close to the leading edge; these lie outside the calibration range, so that the TSP results close to the leading edge for
Fig. 8 Average intensity (counts) in interrogation region vs. time (ms) for all 50 recorded raw images, showing four sample raw intensity im-ages at times shown. (Flow in these imim-ages is fromrighttoleft)
these late times can only be seen as semi-quantitative. How-ever, it should be noted that the used TSP has been shown to work up to 380 K in a laboratory environment (Ondrus et al., 2015).
Fig. 9 TSP temperature results (2D images) over the whole model sur-face for 10 different times during the HEG run. (Flow in these images is fromrighttoleft)
One can now plot the obtained average TSP tempera-tures in the interrogation region (referred to before) for all 46 images and compare the temperature development with the Medtherm results – this comparison is shown in Fig. 10. (Temperature and time error bars for early and late times are shown: for a discussion, see later.) Even though the TSP results aftert=2.5 ms look good and follow the expected trend, nevertheless recall the remarks made earlier. The dif-ference in development of the actual temperature values ob-viously arises from the vastly different thermal properties (ρck) of the Medtherm and TSP paint. This becomes clear from Table 1, whereρ,candkvalues (Eng, 2015) for three
(ρck)1/2 - recall the presence of(ρck)1/2in Eq. 3. These materials have been chosen as ‘representative’: Al repre-sents the test model material, Ni the Medtherm and PMMA (polymethylmethacrylate, a polymer commonly used in TSP) the paint. The values of (ρck) and(ρck)1/2for the Medtherm,
as supplied by the manufacturer, are also shown. (An aside: note that Ni has different (ρck) values to that of the Medtherm.
This is not surprising, since the Medtherm is not made of just Ni, and some abraded dust from its test preparation has also been rubbed into the sensor.) The final row shows the val-ues of(ρck)1/2for the various materials normalized to the value(ρck)1PMMA/2 . As can be seen, mainly the much smaller k (heat conductance) value for PMMA compared with the other three materials leads also to the vastly different(ρck)1/2
values – factors are up to about 40 times larger. The poly-mer based paint (represented by PMMA in Table 1) cannot conduct away the absorbed heat quickly enough, so that the paint surface heats up to higher values compared to those measured by the Medtherm.
Fig. 10 Medtherm and adjacent TSP temperatures vs. time in the HEG run, the latter using TSP calibration data. (Average TSP temperature in the interrogation area – see Fig. 5.)
5.3 TSP heat load results
Using the discretized form of Eq. 3 referred to before, the TSP temperature results shown in Fig. 9 can now be pro-cessed to give the heat loads on the model surface. This local heat load can be determined from the Medtherm measure-ment at its position (see Fig. 5 for location), so that the TSP average temperatures over time in the adjacent interrogation region can be used to determine a local heat load from TSP measurements, withρckinsitubeing varied as a parameter to yield the same heat load from both the TSP and the adja-cent Medtherm measurements – this is effectively an insitu calibration of the TSP paint using the Medtherm. The value
obtained for the TSP paint with this approach wasρckinsitu= 4.5×106kg2K−2s−5. It is again assumed that this value of
ρckpertains over the whole model surface and over the whole time, so that heat loads for all 46 images (fromt=1 ms to 10 ms) over the whole ramp surface can be obtained. (The validity and inherent uncertainties of this assumption will be further discussed in Sect. 5.4.) Ten sample heat load re-sults at different times (0.4 ms, 2 ms, 3 ms, 4 ms, 5 ms, 6 ms, 7 ms, 8 ms, 9 ms and 10 ms), as already shown for tempera-tures in Fig. 9, are shown in Fig. 11. (For the image before gas arrival att =0.4 ms the heat load is obviously zero.) Note that maximum heat loads of 1.6 MWm−2and more are obtained in the upstream (right hand side) positions on the model, even at earlier times (but recall earlier comments on paint calibration and possible damage).
Fig. 11 Heat loads from TSP measurement (2D images) over the whole model surface for 10 different times during the HEG run. (Flow in these images is fromrighttoleft)
As before with temperature (Fig. 10), one can now com-pare the heat load obtained from Medtherm with that from TSP in its adjacent interrogation region. This comparison is shown in Fig. 12. (Average error bars in time and heat trans-fer are shown: see discussion later.)
Here, at times after t≈3 ms (i.e. after the initial dis-turbances seen in the Medtherm results), both heat load re-sults are the same over all times and have average values of 0.73±0.07 MWm−2 for TSP and 0.70±0.08 MWm−2 for Medtherm. But recall: this must obviously be so, since the Medtherm results had been used to calibrate the TSP, so that the agreement has been ‘forced’. Nevertheless, the con-stancy and agreement of heat loads over the whole time for both TSP and Medtherm is very encouraging. The bump in the Medtherm result att=1.6 ms to 2.0 ms correlates well with the smaller one in the TSP result att=2 ms when one considers the TSP negative time correction of 0.4 ms due to the finite paint response time – this will be discussed later in Sect. 5.4.
Table 1 Comparison of material properties (ρ density,cheat capacity,kheat conductance) and the thermal parameter(ρck)1/2for nickel Ni (representing the Medtherm thermoelement), aluminum Al (test model) and PMMA (a typical TSP paint polymer). (Source: see text)
Property Units Medtherm Ni Al PMMA
Densityρ kg/m3 - 8800 2712 950 Heat capacity Jkg−1K−1 - 540 870 1450 Heat conductance Js−1K−1m−1 - 90 110 0.18 ρck J 2m−4K−2s−1 7.95×107 4.3×108 2.6×108 2.5×105 (kg2K−2s−5) p ρck Jm −2K−1s−1/2 8915 20 700 16 000 500 (kgK−1s−5/2) p ρck/p(ρck)PMMA - 18 41 32 1
Fig. 12 Comparison of heat load on the ramp from TSP (in the interro-gation area) and from Medtherm vs. time. Theρckvalue for TSP was obtained by an insitu calibration using the Medtherm result – see text
5.4 Accuracy of TSP temperature and heat load results Here an attempt will be made to address and identify possi-ble sources of errors leading to uncertainties in the derived temperature and heat load results. These sources are both systematic and random. The final goal will be to determine confidence limits for these measured properties; they have already been shown in the foregoing plots as error bars. Spe-cific other sources such as stray illumination (considered the major problem with quantitative TSP in shock tunnels) and particles (as dust) are not considered explicitly here; they have been discussed elsewhere (Beck et al., 2015). However, for the HEG run condition chosen here (lowh0, lowρ∞), the
influence of these sources was minimal and could therefore be neglected here.
5.4.1 Thermal parameterρck: material properties
The TSP paint consists of three layers sprayed onto an alu-minum substrate: the bottom primer layer, a screen layer and finally the active layer consisting of the polymer (here PU) with its embedded luminophores (Eu complex). Sottong
[DLR Cologne, private communication (2015)] carried out material and thermal analyses of the aluminum substrate and these three layers. Each layer thickness and thence its den-sity were determined; Fig. 13 shows a scanning electron mi-croscope (SEM) image of a sectional cut through the alu-minum substrate and its paint coatings, showing the thick-nesses of the three layers and the structure of their surfaces. Heat conductance coefficientskfor the layers and substrate at temperatures from 25◦C to 50◦C were also measured; these values fork(in Wm−1K−1) are plotted as a function of temperature in Fig. 14. The coefficientkfor aluminum is much larger than that for the active layer, by a factor of about 100. However, in the previous estimate ofkin Table 1, the factor was more like 600 (≈110/0.18), which is obviously a huge over-estimate, based on these new measurement re-sults. The conclusion remains the same, however: the main driving force for the different response of the Medtherm and TSP paint to an externally applied heat load is the large dif-ference ink. The largest temperature dependence is shown by the innermost primer and the active layers, where k drops by about 15 % from 25◦C to 50◦C. For the middle screen layer the drop is only about 7 %. One can assume (and para-metric tests here have shown) that for these short test times (<10 ms) mainly (but not solely) the material properties of the outer active layer play the more significant role in influ-encing the heat transfer process.
Fig. 13 SEM (scanning electron microscope) image of cross section through various TSP paint layers, used to determine layer thicknesses (and thence density). Source: see text
Fig. 14 Measured heat conduction coefficients k as a function of tem-perature for the three layers making up the TSP paint (error bar for active layer shown). Note break in the ordinate scale. Source: see text
Finally, using the layer properties determined by Sot-tong, one can obtain a value of ρck and compare it with that determined by the Medtherm insitu calibration of the TSP paint (which wasρckinsitu=4.5×106kg2K−2s−5– see before). Recall that this is different than the approach used by (Nakakita et al., 2003), where very thin paint layers were used (see Sect. 1). (For reference, recall thatρckMedtherm= 7.95×107kg2K−2s−5). Hence, over the temperature range 25◦C to 50◦C, it is estimated that the assumption of a con-stant (viz. average) value of k would also lead to an un-certainty (inaccuracy) in the calculated heat loads of about
±5 % (recall:(ρck)1/2, and notρck, enters into Eq. 3).
Sot-tong measured a constant value ofc=930±45 m2s−2K−1 for all layers and over a temperature range 0◦C to 50◦C. Taking the TSP sample values supplied by Sottong: ρ =
1330 kgm−3, c = 930 ± 45 m2s−2K−1 and
k=2.5±0.2 Wm−1K−1(this value being for just the active layer), one obtains ρckmat = 3.1(±0.3)×106kg2s−5K−2, based just on the material properties. ρckinsitu and ρckmat differ by about 30 %. If one assumes that the second screen layer also plays some role in the heat transfer process, this would lead to larger effective values ofk, lying somewhere in the range 2.3 Wm−1K−1(active layer) and 6.1 Wm−1K−1 (screen), with the subsequentρckmatthen lying between 3.1 and 8.2 kg2s−5K−2.ρckinsitu is right in the middle of this range.cwas measured to be temperature-independent in the range 25◦C to 50◦C. However,cwas measured for the whole sample, and not for the individual layers, which makes it difficult to assess how this simplification may affect the ap-propriate value ofcfor the active layer. In conclusion, then, given these uncertainties in the material properties, and based on present available information, one can nevertheless state that the thermal parameters based on the insitu calibration with the Medtherm are the most reliable. Values based on
material properties have a large degree of uncertainty, which adds support and weight to the insitu method of calibration adopted here.
5.4.2 The interrogation area
As mentioned before, an interrogation area of 15×15 pixels (corresponding to about 2.5 mm×2.5 mm) had been used to compare TSP and Medtherm values – see Fig. 5. This size choice represents a trade-off between two counteract-ing aspects: the area must be large enough to deliver good statistical dynamics (especially at later times where the sig-nals are quite low – see Fig. 5) on the one hand, but, on the other, small enough to avoid too much spatial smearing (the Medtherm has a 1.6 mm diameter, corresponding to an area of about 2.0 mm2). An analysis of the interrogation area for all 50 images led to a maximum value of relative error (based on the mean and standard deviation) of 2 % for the intensities (Figs. 5 and 8), and for temperatures of±2 K at 292 K and±4 K at 340 K (see Fig. 10); similar uncertainties are to be expected for the heat loads. These error estimates are based solely on the statistics of counts in the interroga-tion region. They do not represent the total error/uncertainty – see later.
5.4.3 Correction for time response of the paint
This is potentially a larger source of uncertainty in the final heat load values, influencing both the time and amplitude axes. After excitation by LED light of the Eu complexes in the OV322 paint to an excited electronic state, these Eu molecules relax back to their ground state with a characteris-tic luminescence relaxation timeτ. Generally one assumes a mono-exponential decay (Liu and Sullivan, 2005), so thatτ
represents just one simple decay process characterized by just this one constant. The decay process is temperature-dependent, with temperature influencing the rate of thermal quenching of the excited molecular state: use is in fact made of this phenomenon in the TSP lifetime method, where mea-surement of intensity decay rather than relative intensity is used by Ondrus et al. (2015). They measuredτ as a
func-tion of temperature and pressure for the OV322 paint – see Fig. 15.
Since pressures in the HEG run were around 100 kPa (see Fig. 7 earlier),τ is then seen to be about 330 µs and
200 µs at 25◦C and 50◦C, respectively. These are long times, of duration similar to that of the camera exposure time (tE=
200 µs) in the HEG measurement with CW LED excitation. Hence, for any given exposure window (image), the mea-sured signal is made up of components from fluorescence excited in this window plus decaying fluorescence excited in previous windows. This leads to a time smearing of the
Fig. 15 Luminescence lifetimesτof OV322 paint as a function of tem-perature and pressurep(see text). (Source: Ondrus et al. (2015))
results over some windows, and perhaps also to an influ-ence on the measured intensity in the window (especially so if the fluorescence intensity changes significantly from one window to the next). The following is an assessment of the influence of this effect on ensuing uncertainties in both time and amplitude, and will be carried out based on the follow-ing assumptions3:
1. Fluorescence decay timeτ≈400 µs (=2tE);
2. Decay over several windows is given by just the one de-cay constant;
3. Excitation is via a very short single LED pulse at the start of each window;
4. Only three contiguous windows are considered; 5. This analysis is considered to apply for a large number
of single pulse excitations over the whole window (viz. simulating CW excitation);
6. AreasA under the curves (see Fig. 16) are assumed to scale with initial intensities (see text).
The sketch of fluorescence decay curves in Fig. 16 (note: ordinates are not drawn to scale) show in the abscissa adja-cent exposure time windows of widthtE(wheretE=200 µs).
The signal measured by the camera in windown(in green), is made up of the sum of contributions from excitation in windows (n−2), (n−1) andnitself, and will now be con-sidered. For initial simplification, it is assumed that excita-tion in each of the windows (n−2), (n−1) andnoccurs at the beginning (e.g. by a very short LED pulse), with ensuing fluorescence decay over three subsequent windows to the re-spective levels 1/e3/2, 1/e1/2and 1/eof the initial fluores-cenceIi. For example, fluorescence from window (n−2) has 3It should be noted, that these assumptions were made in order to assess the measurement uncertainty for the described measurement case. It is not meant to be a general and rigorous analysis for all possi-ble measurement conditions.
Fig. 16 Fluorescence decay curves over contiguous windows assum-ing sassum-ingle short pulse excitation at the beginnassum-ing of each window. Con-stant (Case 1) and changing (Case 2) initial fluorescence intensities for the 3 windows are considered. (See text.) The areasApertain to those under the corresponding curves for fluorescence decay from windows (n−2), (n−1) andn
fallen to a value of 1/e3/2≈22 % of its original value at the end of windown; contributions from even earlier windows are not included in this assessment. Furthermore, for sim-plification, it has been assumed thatτ≈2tE(this is
approxi-mately correct at the early times). The intensity measured by the camera in windownis thenA(n−2)3+A(n−1)2+An1 (see Fig. 16), namely:
Itot=In−2 Z 3tE 2tE e(−t/2tE)dt+I n−1 Z 2tE tE e(−t/2tE)dt +In Z tE 0 e(−t/2tE)dt (4)
whereIn−2,In−1 andInare the initial fluorescence
intensi-ties in their respective windows. For Case 1 in Fig. 16, it has been assumed thatI=In−2=In−1=In, so that Eq. 4
simplifies to: Itot=I Z 3tE 2tE e(−t/2tE)dt+ Z 2tE tE e(−t/2tE)dt+ Z tE 0 e(−t/2tE)dt =I Z 3tE 0 e(−t/2tE)dt (5) Hence, from Fig. 16:
An3=In−2 Z 3tE 2tE e(−t/2tE)dt ≡A(n−2)3 An3=In−2 Z 2tE tE e(−t/2tE)dt ≡A(n−2)2
In other words, the measured signal would be the same as that which arises from capturing the fluorescence from just the one excitation at the start of window n for the three fol-lowing windowsn,n+1 andn+2. In Fig. 16 Case 1 this is shown pictorially:An1+An2+An3=An1+A(n−1)2+
A(n−2)3. Case 1 is the “trivial” case and applies only for equal initial fluorescence intensities. In Case 2 these intensi-ties are not equal, but, for the measurements here, falling, as shown in Fig. 16 Case 2. (Obviously increasing temperature over time leads to decreasing fluorescence intensity.) Hence the contributions from windowsn−1 andn−2 to intensity measured by the camera in windownare larger, leading to a measured intensity which is too high:An3<A(n−2)3and
An2<A(n−1)2. The influence of this effect on the mea-surement uncertainty in window n will now be assessed, based on the measured differences between the intensities
In−2,In−1 andIn, as given by the results shown earlier in Fig. 5: here one sees that intensities drop by about 8 % per window over the first three windows after gas arrival, where this drop is largest:In−2/In−1≈In−1/In≈0.92. Assuming that the relative areasA(n−2)3/An3andA(n−1)2/An2(see Fig. 16 Case 2) scale with the initial intensities, namely:
A(n−2)3 An3 =In−2 In =0.922 A(n−1)2 An2 =In−2 In =0.92
the total intensityItotmeasured in windownthen becomes: Itot=An1+A(n−1)2+A(n−2)3 =An1+An2· In−1 In +An3· In−2 In =An1+0.92·An2+0.922·An3
Now evaluate the integralsAn1,An2andAn3to get:
An1:An2:An3=1 : 1
e1/2 : 1
e3/2≈100 : 60 : 36
The discrepancies in the total signalAn1+An2+An3arise from the abovementioned differences forAn2vs.A(n−1)2 and forAn3vs.A(n−2)3, which correspond to, respectively,
(1−0.92) =0.08=8 % and (1−0.922) =0.15=15 %. This leads to a total signal of 100+60+36=196, while the correction factor (or uncertainties) amount to 60·(−0.08) +
36·(−0.15) =−10. The relative uncertainty is therefore about−10/196=−0.05=−5 %. This is strictly not an er-ror, but corresponds to a systematic discrepancy or a cor-rection factor. Note that the sign is negative (since the inten-sity is dropping). The above discussion and estimations were based on an assumption of single short pulse LED excitation at the beginning of each window. However, CW LED exci-tation was used in the experiment. If one considers the CW excitation over a window to be made up of an infinite (viz. a large number) of single pulse excitations, then the conclu-sions reached here should still be valid, since each single pulse excitation at times within the window would behave and be evaluated in a similar way as above. The total uncer-tainty in amplitude (intensity), based only on those issues discussed in the preceding subsections, is hence estimated
to be 2 % and−7 %. The uncertainty in the time domain, based on the model calculations discussed above, is−2tE,
i.e. about−0.4 ms. These errors/uncertainties are included in the respective plots shown earlier – note they are asym-metrical.
5.4.4 Normalized TSP and Medtherm temperatures
Finally, a check on the performance of the TSP paint is to plot normalized temperatureT vs. timet, and assume that
T = f t1/2, or T2= f(t) – as suggested from Eq. 3. If the behaviour of TSP (especially its time response) were to have a strong effect, one would expect the plots for TSP and Medtherm to show different trends over time. Fig. 17 shows a plot of[(Tt−T0)/(Tmax−T0)]2vs.t, where T0= temperature before gas arrival,Tmax=temperature at 10 ms
andTt=temperature at timet. Apart from the bumps in the
Medtherm plot at early times, both plots show very simi-lar behaviour, demonstrating that TSP, in spite of its simi-larger time response (compared with Medtherm), can still deliver meaningful results of temperatures and thence of heat load.
Fig. 17 TSP and Medtherm temperatures T vs. time t, plotted normal-ized to minimum and maximum values, and assumingT = f t1/2 (viz.T2=f(t)): see Sect. 5.4.4.T0is the temperature before gas ar-rival;Tmaxis the temperature at 10 ms. For error/uncertainty estimate: see Fig. 12
6 Conclusions
This work has demonstrated the usability of TSP to measure temperatures on a surface in a hypersonic, short-duration flow, and therefrom to calculate the heat load, making use of those assumptions generally applied to these types of flows. Both temperature and heat load results on the surface of a ramp model placed in a MachM=7.4 HEG flow were shown. A Medtherm coaxial thermocouple situated at one
position on the model was used to calibrate the TSP paint (viz. to obtain the thermal parameterρckfor the paint). An average heat load in the interrogation region of 0.73±0.07 MWm−2has been measured. A further more de-tailed discussion of sources of error and uncertainty in the final results was given.
Acknowledgements The authors are grateful to the follow-ing for their assistance: Werner Sachs (DLR, now retired) for help in data processing using the DLR in-house code nToPas; Marco Costantini (DLR G¨ottingen) for invaluable contributions to determining the TSP paint material prop-erties; Reinhard Sottong (DLR Cologne) for carrying out measurements of material properties on samples of paint; Jan Martinez Schramm (DLR G¨ottingen) for test preparation support; Vlado Ondrus (University of Hohenheim) for de-velopment of the paint OV322; Uwe Fey (DLR G¨ottingen) for construction of the LED multi-lens array.
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